"The larger the sensor the blurrier the background can be, and this also changes the distance at what you can make a picture of something and still have a blurry background."
Blur is totally determined by optics and has no direct relationship to sensor / film area.
So yes, practically speaking, a camera with a much larger sensor / film area does allow you to take pictures with a much more narrow depth-of-field.
The size of the circle-of-confusion depends also on the degree of enlargement and viewing distance in the final product - i.e. what looks sharp when viewed at arm's length on a phone with a Retina display can look not-sharp when cropped and enlarged to 20x30 and seen up close.
You’re both correct—optics are constrained by sensor size, so while the amount of background defocus is determined directly by optics, it is determined indirectly by sensor size.
The amount of blur at infinity is proportional to the ratio of the aperture size (e.g. measured in mm) to the subject size (e.g. measured in mm). For a given lens design, the aperture size is proportional to the sensor size.
You do get higher aperture numbers for smaller sensors but we’re talking about a factor of, say, 2x weighed against much larger numbers. This is just because wide-open lenses are impractical to manufacture at larger sizes (weight goes up with the cube, after all).
I see phone cameras with lenses at like ƒ/2.2 or something thereabouts and it’s not radically different from what you’d see on larger cameras until you get to LF, but if you dive into vintage LF lenses you’ll see “barrel lenses” with crazy, like, ƒ/2 designs for shooting on LF film. These are not scaled-up versions of sensible, modern designs. Instead, they are really old designs, and they are not gonna be sharp.
You typed out what I should have - I accidentally wasted people's in this thread by being vague
I'm sorry, but no. There is a direct relationship between exit pupil image size and the size of the sensor.
>A crop-sensor camera also comes in handy for macro shots. Recall that depth of field (DOF) is the distance between the closest and furthest parts in an image that will appear in focus. At the same aperture and for the same field of view, an APS-C sensor will have a higher depth of field than with a full frame camera.
I read your comment as saying that the exact same 50mm f/2 lens will produce less blur on an MFT body than on a full-frame body. That'd be a narrower FOV (~100mm equivalent) but the same blur as full frame. Perhaps I misinterpreted?
To see this, imagine that you're focused to a distance of 9 meters. That means that all the light from any point in the plane that is 9 meters away gets focused on one spot on the sensor, with this spot on the sensor corresponding to the location on the plane. Now imagine what happens with the light from a point 10 meters away. On the way to the sensor, all the light rays from this point will have to pass through the plane that is 9 meters away, and will then behave just as if they originated from that 9-meter-away plane. Since that plane is in focus, these rays will show up on the sensor in positions corresponding to where they were in the 9-meter-away plane.
Now imagine where those rays from 10 meters away that end up on the sensor actually are when they reach the 9-meter-away plane. Suppose the absolute aperture (diameter of lens) is 20mm. The rays that hit the lens (and then the sensor) starting from 10 meters away form a cone, which spreads out to 20mm at the camera. So at 9 meters away, 1/10 that distance, the cone will have spread out 1/10 as much, which is 2mm. So single points at a distance of 10 meters look just like disks 2mm wide at 9 meters. That's the extent of out-of-focus blur.
How blurry that seems to the viewer of the final image depends on the field of view, which for a fixed focal length depends on the sensor size. With a small sensor, the field of view at 9 meters might be only 200mm, and 2mm looks fairly blurred. With a large sensor, the field of view at 9 meters might be 2000mm, and a 2mm disk might look almost like a point to the viewer.
EDIT: I realize now that the concluding paragraph may be confusing, since it seems to say that it's the small sensor that will have more blur. The problem is that I shouldn't have compared images with different fields of view - when deciding which camera to use to take a picture you have in mind, you of course envision using lenses for each camera that will give the same field of view, as appropriate for the result you are trying to achieve. Looked at that way, one can see that with the field of view fixed, an absolute aperature of 20mm will correspond to a smaller f-stop for a camera with a small sensor size than for a camera with a larger sensor. For instance, a 100mm focal length lens with a 20mm aperature is an f/5 lens. With a sensor 1/10 as large, one would need a 10mm focal length lens for the same field of view, which would need to be f/0.5 to have a 20mm aperture, if one want to produce the same background blur. It's either impossible or extremely expensive to get an f/0.5 lens.